Folks,
Time for the biennial spiel. The theory behind the tax exemption for private social clubs is that they ARE social clubs, not businesses open to the public, and support themselves by pooling the member's funds. There is therefore no income to tax. However, clubs do earn outside income, and the IRS has set a safe harbor that a social club can earn 15 percent of gross revenue from nonmembers. Any more, and it looks like a business that supports member activities from public money, and therefore is taxable.
There's a lot of technical stuff, but that's the theory (and not legal advice).